1. topper — de Vaan
topper 'quickly' (Andr.+). Pit *peri 'through, across', *pero- 'on the other side'. It. cognates: Vea per [prep. + ace] 'for', U. -per, -pe, -per,[postpos. + abl.] 'for\ O.per-, Pael.pe-, IJ.per-, per-, SPic. per- 'before, past* < *pers < *per + -s; O. perum 'without' < *pero- 'on the other side'; O. pert, U. pert [prep. + ace] 'until, near', O. pert-, -pert, U. -per, -per 'untir or 'near(ly)' < *per-ti. PIE *peri … — [de Vaan, s.v. topper, p. 473]
2. topper — de Vaan
topper 'quickly' [adv.] (Andr.+) Pit. */orf? */otf? Lat topper is generally regarded as a unfverbation of *tod (nom.acc.sg.n. of the stem */o- 'that') and the suffix -per. Whether the first element really was *tod remains uncertain: in view of the meanings initial tot 'that many' seems equally possible. Bibl.: WH II: 692, EM 695, IEW 1086f, Leumann 1977: 476, Livingston 2004: 17-22. —> so-, tam, toU turn — [de Vaan, s.v. topper, p. 638]
3. topper — Lewis & Short
topper, adv.contr. from toto opere,
I with all diligence, speedily, forthwith (anteclass.; cf.: ab ultimis et jam oblitteratis repetita temporibus, qualia sunt topper et antigerio, etc.,
Quint. 1, 6, 40): topper citi ad aedes venimus Circae, Pac. ap. Fest. p. 352 Müll.; so Naev., Enn., Att., Cael. ib.